leetcode162. Find Peak Element (O(lgn)复杂度寻找峰值)

A peak element is an element that is greater than its neighbors.

Given an input array where num[i] num[i+1], find a peak element and return its index.

The array may contain multiple peaks, in that case return the index to any one of the peaks is fine.

You may imagine that num[-1] = num[n] = -.

For example, in array [1, 2, 3, 1], 3 is a peak element and your function should return the index number 2.

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Note:Your solution should be in logarithmic complexity.

思路:

为什么能lgn。。。

首先要想明白,这样的峰值是一定存在的(因为最左最右已经负无穷了。

如果中间元素的值,比它右边相邻元素的小,说明什么呢?

说明右边区间一定存在峰值。

为什么?

现在a[mid]<a[mid+1]

如果a[mid+1]>a[mid+2],那么 a[mid+1]就是峰值

如果a[mid+1]<=a[mid+2],那么可以继续缩小区间,到[mid+2,n-1]

由于a[n]为负无穷,因此至少会出现一个 a[x]>a[x+1]的情况,此时a[x]就是峰值。

想清楚了这点就好办了。二分就好。

 

作者: CrazyKK

ex-ACMer@hust,researcher@sensetime

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